@article{Mhagama2024, 
author = {Lyimo Sygbert Mhagama and Muhammad Faisal Nadeem and Mohamad Nazri Husin},
title = {On the edge metric dimension of some classes of cacti},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {16422-16435},
keywords = {cactus graphs, edge metric generator, edge metric dimension},
url = {https://www.sciopen.com/article/10.3934/math.2024795},
doi = {10.3934/math.2024795},
abstract = {The cactus graph has many practical applications, particularly in radio communication systems. Let    G  =  (  V  ,  E  ) be a finite, undirected, and simple connected graph, then the edge metric dimension of    G is the minimum cardinality of the edge metric generator for    G (an ordered set of vertices that uniquely determines each pair of distinct edges in terms of distance vectors). Given an ordered set of vertices              G        e    =  {      g    1    ,      g    2    ,  .  .  .  ,      g    k    } of a connected graph    G, for any edge    e  ∈  E, we referred to the    k-vector (ordered    k-tuple),    r  (  e      |              G        e    )  =  (  d  (  e  ,      g    1    )  ,  d  (  e  ,      g    2    )  ,  .  .  .  ,  d  (  e  ,      g    k    )  ) as the edge metric representation of    e with respect to        G    e  . In this regard,              G        e   is an edge metric generator for    G if, and only if, for every pair of distinct edges        e    1    ,      e    2    ∈  E implies    r  (      e    1        |              G        e    )  ≠  r  (      e    2        |              G        e    ). In this paper, we investigated another class of cacti different from the cacti studied in previous literature. We determined the edge metric dimension of the following cacti:        C    (  n  ,  c  ,  r  ) and        C    (  n  ,  m  ,  c  ,  r  ) in terms of the number of cycles    (  c  ) and the number of paths    (  r  ).}
}